I found this Article to be interesting and informative. It all makes sense to me, and I have no major criticisms. I would like to mention a different approach.

An important distinction not mentioned (made in experimental economics and other fields) is that between second-party and third-party punishment, abbreviated as 2pp and 3pp. In 2pp, the victim punishes the injurer. In 3pp, a third party does. In experiments it is often simply another subject in the experiment. In real life, it is often the state, or someone given the power to punish in order to enforce the rules of a group, although it may be simply an uninvolved third person.

Roughly, the rise of government over human history coincided with the replacement of 2pp by 3pp. Modern governments, when they can assert their authority, usually forbid 2pp, calling it “taking justice into your own hands” or “vigilante justice” (which can also include 3pp but may also be 2pp by an offended group). The norms of 2pp tend to be based on retribution, although of course this is correlated with (at least specific) deterrence, so that both rationales can be used at once, whichever is primary. (“I’ll teach that SOB not to mess with me anymore. And, anyway, he deserves what he’s going to get.”) The norms of 3pp arise less from the idea of retaliation, since the punisher is not the victim, and are thus more open to other rationales, such as the standard utilitarian rationales of deterrence, incapacitation and rehabilitation, although explicit recognition of these norms came long after state power was well consolidated around the world.

In general people tend to see the replacement of 2pp by government-controlled 3pp as a reform. Culture moves from feuds and warring gangs to a more orderly state of affairs.
For international law, including (but not limited to) international criminal law, we are in transition. Relations among nations have, through much of history, been almost entirely based on 2pp. (The exceptions are empires that encompassed many otherwise-warring states.) Very new is the idea that 3pp could be meted out for crimes within a nation that itself did not punish them. We may be seeing the first steps in construction, brick by brick, of a world government, including a justice system based on 3pp. The first steps are necessarily tentative, dealing with only the most egregious crimes. Much the same tentativeness exists with other aspects of international law. For example, trade agreements often specify the rules for 2pp but do not replace it with 3pp.

Because of this instability and tentativeness, international criminal law right now may not resemble its final form. Thus, as Woods points out, expectations for appropriate punishment may be based more on the norms of 2pp, because that is already widely used.

Also, the use of 3pp often occurs against a background of tit-for-tat 2pp. Actions that may seem horrible when viewed on their own become more normal when they are seen in the context of an ongoing feud based on 2pp. Pick, for example, any random massacre of Hindus by Muslims, or of Muslims by Hindus, and you break into a cycle that has been going on for over 1,000 years, with each side happy to explain to you why the other side deserved what it got, based on a self-serving account of history. As Woods points out, the simple use of retributive punishment of the offender of the moment may seem unfair. To assert its power, a budding international regime may want to act more like the teacher who breaks up a fight on the playground: “Just stop. Now. I don’t care who started it.” The need for such an attitude arises from the existence of a transition from 2pp to 3pp.

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